A Non-Hausdorff Completion
The Abelian Category of C-complete Left Modules over a Topological Ring
Nonfiction, Science & Nature, Mathematics, Topology, Algebra
| Author: | Saul Lubkin | ISBN: | 9789814667401 |
| Publisher: | World Scientific Publishing Company | Publication: | May 28, 2015 |
| Imprint: | WSPC | Language: | English |
| Author: | Saul Lubkin |
| ISBN: | 9789814667401 |
| Publisher: | World Scientific Publishing Company |
| Publication: | May 28, 2015 |
| Imprint: | WSPC |
| Language: | English |
This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M^ can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.
The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces — by replacing the cumbersome "complete tensor product" of p-adic Banach spaces, with the more sophisticated "C-complete tensor product", discussed in this book.
It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.
Contents:
- Admissible Topological Rings
- The C-completion of an Abstract Module over a Topological Ring
- The Case of an Admissible Topological Ring
- The Higher C-completions
- The Direct Sum and Direct Limit of C-complete Left A-modules
- Ext and Tor in the Category of C-complete Left A-modules
Readership: Graduate students and researchers in algebra and number theory, geometry and topology.
Key Features:
- The material in this book is entirely new and original — there are no competing titles
This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M^ can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.
The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces — by replacing the cumbersome "complete tensor product" of p-adic Banach spaces, with the more sophisticated "C-complete tensor product", discussed in this book.
It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.
Contents:
- Admissible Topological Rings
- The C-completion of an Abstract Module over a Topological Ring
- The Case of an Admissible Topological Ring
- The Higher C-completions
- The Direct Sum and Direct Limit of C-complete Left A-modules
- Ext and Tor in the Category of C-complete Left A-modules
Readership: Graduate students and researchers in algebra and number theory, geometry and topology.
Key Features:
- The material in this book is entirely new and original — there are no competing titles
